I imagine that they're mostly targeting sports where the university doesn't typically offer (full) scholarships. That's probably why basketball and football aren't included.
There's also the possibility that the student wouldn't be obligated to play the sport in order to get the scholarship money. Most students want to play their sport anyways.
That's smart because in fact football, specifically football, correlates the worst with military (according to whatever sources I happen to have). Every other sport is better for military training than football. There may be obscure exceptions, like things that can barely be called sports, but that's irrelevant because of their being obscure exceptions. Football is like...about explosiveness, right?
I mean I had a keen interest in football growing up in Chile, distaste for British sports, but beyond having a little real football football myself that was impossible for any other students of my school to acquire, there was literally nothing I could do to actually play this sport. Nobody played "fútbol americano" anywhere...OK thinking back, there were some tag football games in middle school, and we got together and played real football with real tackles just for the love of this sport in high school a little bit, secretly...so fun. Fucked up tackles, spinal.
Literally zero opportunities though. Just literally none. I heard much later there were two actual teams in the city, made of who knows whom.
Baseball there was some of that, it was an American school so they had enough players for two teams, it was really fun...just fun to play an American sport, patriotism is fun! Just fun to do American things like a normal American kid, how was I supposed to know baseball was a boring sport, I had a great time! Dreaming of returning to America, the land of my birth[1]. I just dreamed of playing, never of being on a league, just actually playing. There was a lot of basketball in Chile, that I will say. There there were some opportunities.
But that's not what military training is about really. So you have to fund more obscure sports. Like track, running a two-minute 8 [hundred meter race] that's perfect, hey a platoon of that...and the thing too is it just isn't as theatrical as football or basketball, it's not good television. I've competed in more 8's than I've watched. Grit isn't glamorous.
[1] Which I did, by beating the system at college admissions. So I was never going to be a truly good student, strictly because I was too defective for that, brutal and completely untreated learning disability. But what I could do was want it more, focus on what was essential, yeah being smart ADD notwithstanding, working like FUCK just white-knuckle it, focus on giving admissions committees what they truly wanted, and sacrifice every other metric as though it were gasoline.
There's also the possibility that the student wouldn't be obligated to play the sport in order to get the scholarship money. Most students want to play their sport anyways.